1302.7185 (Tarek A. Elsayed)

Generalized Fermat principle for classical and quantum systems    [PDF]

Tarek A. Elsayed

The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and propose a new variational principle in classical phase space and quantum Hilbert space that mimics Fermat principle in optics. The state of a many-body classical (quantum) system follows a trajectory in the phase (Hilbert) space that extremizes the time functional. The classical Hamilton's equations of motion and the quantum Schrodinger's equation are shown to lead necessarily to a stationary time functional. A plethora of other unconventional variational principles centred on the geometry of the dynamical evolution, and inspired from Fermat principle are discussed in this paper.

View original: http://arxiv.org/abs/1302.7185